On the propagation of a quasi-static disturbance in a heterogeneous, deformable, and porous medium with pressure-dependent properties

Abstract

Using an asymptotic technique, valid when the medium properties are smoothly varying, I derive a semianalytic expression for the propagation velocity of a quasi-static disturbance traveling within a nonlinear-elastic porous medium. The phase, a function related to the propagation time, depends upon the properties of the medium, including the pressure sensitivities of the medium parameters, and on pressure and displacement amplitude changes. Thus, the propagation velocity of a disturbance depends upon its amplitude, as might be expected for a nonlinear process. As a check, the expression for the phase function is evaluated for a poroelastic medium when the material properties do not depend upon the fluid pressure. In that case, the travel time estimates agree with conventional analytic estimates and with values calculated using a numerical simulator. For a medium with pressure-dependent permeability I find general agreement between the semianalytic estimates and estimates from a numerical simulation. In this case the pressure amplitude changes are obtained from the numerical simulator. Copyright 2011 by the American Geophysical Union.